This function plots the sample mean as the sample size grows to check whether the sample mean approaches to the population mean.
np points are plotted to denote the distribution of the sample mean;
we will observe that the range of the sample mean just becomes smaller and
smaller as the sample size increases and ultimately there will be an obvious
trend that the sample mean converges to the population mean mu.
The parameter nmax in ani.options means the maximum
sample size.
library(animation)
ani.options(interval = 0.01, nmax = 150)
lln.ani(pch = ".")
## chi-square distribution; population mean = df
lln.ani(FUN = function(n, mu) rchisq(n, df = mu), mu = 5, cex = 0.6)
The sample mean approaches to the population mean as the sample size n grows
Donate
As a freelancer (currently working as a contractor) and a dad of three kids, I truly appreciate your donation to support my writing and open-source software development! Your contribution helps me cope with financial uncertainty better, so I can spend more time on producing high-quality content and software. You can make a donation through methods below.
-
Venmo:
@yihui_xie, or Zelle:[email protected] -
Paypal
-
If you have a Paypal account, you can follow the link https://paypal.me/YihuiXie or find me on Paypal via my email
[email protected]. Please choose the payment type as “Family and Friends” (instead of “Goods and Services”) to avoid extra fees. -
If you don’t have Paypal, you may donate through this link via your debit or credit card. Paypal will charge a fee on my side.
-
-
Other ways:
WeChat Pay (微信支付：谢益辉) Alipay (支付宝：谢益辉) 
When sending money, please be sure to add a note “gift” or “donation” if possible, so it won’t be treated as my taxable income but a genuine gift. Needless to say, donation is completely voluntary and I appreciate any amount you can give.
Please feel free to email me if you prefer a different way to give. Thank you very much!
I’ll give back a significant portion of the donations to the open-source community and charities. For the record, I received about $30,000 in total (before tax) in 2024-25, and gave back about $15,000 (after tax).